What was Big Willy Shakes going for?
Back in Big Willie's day, "night-owl" just meant a plain old owl. Why did they add the "night" in front? Well, owls stay up at night. It's as simple as that. Shakespeare came up with the figurative meaning of someone staying up all night in his long poem, Rape of Lucrece.
Richard II says that owls shriek when morning comes because there is nothing left for them to do. Who wants a sleepy owl when there's a singing bird (lark) around? No one does, that's who. In the same way, no one seems to want Richard around any more. He's old news—a night-owl in a world of larks.
See, Bolingbroke is waging a war with Richard, and he knows it too. Richard's already sealed his fate by saying, "you know what? I think I'm about as useful as an owl during the daytime." So… not useful at all. And he's right.
Richard's speech is prophetic. He does end up getting bumped off the throne, thrown in the slammer, and murdered. Yikes. Maybe he shouldn't have banished Bolingbroke, but it's too late for that now.